The squaring of 'zero'

The squaring of 'zero'

By Andrew Hass

14 Jun 2012

Negation has ascended into the imagination of our culture and society not necessarily as something to be scorned or regretted, but as something with which to be, in some cultural, philosophical, or even religious form, reconciled, says Dr Andrew Hass. But before we can understand how this figure might work its way into and through our present world, we need first to ask, whence 'zero'? For its history is by no means one we might expect.

We have been thinking in the Critical Religion research project (http://www.criticalreligion.stir.ac.uk/[9]) about the nature of negation, and how it has ascended into the imagination of our culture and society not necessarily as something to be scorned or regretted, but as something with which to be, in some cultural, philosophical, or even religious form, reconciled.

Of course its primary symbol, in terms of production, is the figure of zero. But before we can understand how this figure might work its way into and through our present world, we need first to ask, whence zero? For its history is by no means one we might expect.

If we go back to the beginnings of scripted language and numerology, zero was not necessarily there at the outset. The ancient Egyptians developed a system of accounting based on a pictography – notation in pictures. Of course with pictographic language, a positive referent is needed to which one can point in the world. But when it comes to an understanding of nothing, pictography is ill-suited. For how does one picture nothing?

The whole point of nothing is that it cannot be seen. To envision it, it must be turned into something abstract, like a concept, beyond pictures. Now we know the ancient Egyptian civilisation was famed for mathematics – their pyramids proved their excellence at geometry, the configuration of shapes through mathematical precision. And yet in all this excellence, they never required zero in their computations, and therefore never developed any corresponding symbol.

This says as much about their cosmological and theological understanding as it does about their mathematical acumen. For from the Book of the Dead we learn that death was not about returning to an abyssal place of nothing. Significantly, the ferryman who transported the dead soul across the river to the netherworld denied passage to anyone “who does not know the number of his fingers”. This showed the importance of accounting: as accounting was important for the Pharaohs who exacted some form of taxation upon their people, so too in death it is important to know how to account for oneself. (One must be counted, it appears, even in the afterlife.) And so there was a deliberate avoidance of nothing, because nothing troubles the system of accounting, whether financial, philosophical or religious.

It is therefore not surprising that the Egyptians developed such a sophisticated technique of bodily preservation upon death. Mummification, we might say, is a gesture against the void, or it is a gesture of containment and preservation against that which negates us. The pyramids, we remember, functioned as tombs. So it is that the shape of O, as zero, figures neither in the pyramidical shape nor in the afterlife. Zero would be a perilous ticket for the ferryman.

The ancient Greeks too did not have a symbol for zero. This might seem even more incredible, since they had a distinct predilection for conceptualising. But as early as the Presocratics, those philosophers who preceded Socrates and Plato, there was a general repulsion to the concept of nothing. Parmenides, for example, talked much about the concept of a changeless One, but was adamant about the impossibility for “what is not” to exist, or even to be thought of. He therefore instructs us not to think on it. And for the most part the Greeks heeded his instruction, and shunned thinking about the nothing altogether.

If we consider Greek thinking from the Presocratics onwards, we know that so much emphasis is placed on ratio, on ordering things in relation to one another. This is inherent in their term “logos”, which is accompanied by the notions of rationality and proportionality. (Ratio is part of the rational.) Reality then, underwritten as it is by logos, must remain accountable, or countable. The Pythagoreans were extreme in championing countability, to the point where reality in fact becomes number. But zero does not figure in this reality. In Greek logic (the logic of logos) zero cannot be a number as such. For the “0” introduces a void, and voids, by definition, cannot be counted. It is void of all quantification. If the cosmos is structured upon the logos, even a quasi-divinised Logos, which allows us to think rationally about it, to speak of it and (ac)count for it, it must remain positive.

The idea of the nothing or of the negative cannot be part of the equation or the calculation. Thus like the Egyptians, the Greeks also did not develop any symbol for the naught in their numerology.

Nor did the Romans. Having been Hellenised by the Greeks, the Roman numeral system developed conspicuously without any figure for zero. And this from an empire who took accounting, and indeed taxation, to new and perfected heights across an extraordinary range of geography and peoples.

This absence is felt throughout Roman culture, even in something as functional as their clocks: the Roman sundials were without a zero point, which means time was always positive – a god, in fact, like the Greek’s Chronos. This despite the fact that the sundial’s circular path outlined an “O”, the figure used elsewhere for the sign of nothing – a sign of the times to come, we might say, when the Roman numeral system proved inadequate, and the West had to turn and face its own nothing.

This is part one of a two-part article. Part two will appear early next month.

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This article is one of a continuous series appearing on Ekklesia through our association with the University of Stirling Critical Religion[13] group blog. CR is a research project[9] bringing together academics from a wide range of backgrounds to explore the way 'religion' is employed as a a marker, construct and category in public and intellectual discourse. You can also follow Critical Religion on Twitter: http://twitter.com/StirCritRel[14]